Minimum Automatic Differentiation

minimum_autodiff.ipynb

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    "Minimum Automatic Differentiation"
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   "source": [
    "import numpy as np\n",
    "def mul(x, y):\n",
    "    a, b = x\n",
    "    c, d = y\n",
    "    return a*c, a*d + b*c\n",
    "\n",
    "def add(x, y):\n",
    "    a, b = x\n",
    "    c, d = y\n",
    "    return a + c, b + d\n",
    "\n",
    "def cos(x):\n",
    "    a, b = x\n",
    "    return np.cos(a), - np.sin(a)*b\n",
    "\n",
    "def sin(x):\n",
    "    a, b = x\n",
    "    return np.sin(a), np.cos(a)*b\n",
    "    \n",
    "def log(x):\n",
    "    a, b = x\n",
    "    return np.log(a), b/a "
   ]
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   "source": [
    "Consider \n",
    "$f(x) = \\log{(\\cos{x} \\sin{x})} + \\sin{x}$\n",
    "and derive its derivative at $x=1.0$"
   ]
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   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "f = lambda x: add(log(mul(cos(x),sin(x))),sin(x))\n",
    "df = lambda x: f([x,1.0])"
   ]
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      "text/plain": [
       "(0.05324076815279066, -0.37501280285243144)"
      ]
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     "execution_count": 9,
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     "output_type": "execute_result"
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   ],
   "source": [
    "df(1.0)"
   ]
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   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "g = lambda x: f(f(x))\n",
    "dg = lambda x: g([x,1.0])"
   ]
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   "execution_count": 14,
   "metadata": {},
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      "text/plain": [
       "(-2.8816056725768977, -7.391555094461485)"
      ]
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     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "dg(1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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